Topological extensions of product spaces

NEARNESSES AND To - EXTENSIONS OF TOPOLOGICAL SPACES

ABSTRACf. In [3], Reed establishes a bijection between the (equivalence classes of) principal Tt-extensions of a topological space X and the compatible, cluster-generated, Lodato nearnesses on X. We extend Reed's result to the To case by obtaining a one-to-one correspondence between the principal To-extensions of a space X and the collections of sets (called "t-grill sets") which generate a cer...

Openly Factorizable Spaces and Compact Extensions of Topological Semigroups

We prove that the semigroup operation of a topological semigroup S extends to a continuous semigroup operation on its the Stone-Čech compactification βS provided S is a pseudocompact openly factorizable space, which means that each map f : S → Y to a second countable space Y can be written as the composition f = g ◦ p of an open map p : X → Z onto a second countable space Z and a map g : Z → Y ...

REDUNDANCY OF MULTISET TOPOLOGICAL SPACES

In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^star(U),sqsubseteq)$ and $(Ds(varphi(U)),subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.

σ-Normality of Topological Spaces

Properties of the Product of Compact Topological Spaces

One can prove the following proposition (1) For all topological spaces S, T holds Ω[: S, T :] = [:ΩS , ΩT :]. Let X be a set and let Y be an empty set. Note that [:X, Y :] is empty. Let X be an empty set and let Y be a set. Observe that [:X, Y :] is empty. We now state the proposition (2) Let X, Y be non empty topological spaces and x be a point of X. Then Y 7−→ x is a continuous map from Y int...